If the spell being copied is modal (that is, it says "Choose one —" or the like), each copy will have the same mode. You can't choose a different one.

Howl of the Horde creates a delayed triggered ability that triggers when you cast your next instant or sorcery spell that turn. The raid ability creates a second, identical delayed triggered ability. Each of these will create a single copy of the next instant or sorcery spell you cast during that turn. If you don't cast another instant or sorcery spell during that turn, both delayed triggered abilities will cease to exist.

If the spell being copied has an X whose value was determined as it was cast (like Crater's Claws has), each copy will have the same value of X.

When either ability resolves, it creates a copy of the instant or sorcery spell. You control each copy. Each copy is created on the stack, so it's not "cast." Abilities that trigger when a player casts a spell won't trigger. The copy or copies will then resolve like normal spells, after players get a chance to cast spells and activate abilities.

The delayed triggered abilities will copy any instant or sorcery spell, not just one with targets.

Each copy will have the same targets as the spell it's copying unless you choose new ones. You may change any number of the targets, including all of them or none of them. If, for one of the targets, you can't choose a new legal target, then it remains unchanged (even if the current target is illegal). You can choose different targets for each copy.

Raid abilities evaluate the entire turn to see if you attacked with a creature. That creature doesn't have to still be on the battlefield. Similarly, the player, planeswalker, or battle it attacked doesn't have to still be in the game or on the battlefield.

Raid abilities care only that you attacked with a creature. It doesn't matter how many creatures you attacked with or which player, planeswalker, or battle those creatures attacked.